RC Filter Calculator
Enter the resistance and capacitance of your RC circuit to find the -3 dB cutoff frequency, RC time constant, capacitive reactance, total impedance, phase shift, and voltage gain at any signal frequency. Choose low-pass or high-pass mode, and use reverse-solve to find R or C from a target cutoff frequency.
What is an RC filter and how does it work?
An RC filter is one of the simplest and most widely used circuits in electronics. It consists of a resistor and a capacitor connected in series. Because the capacitor's impedance is inversely proportional to frequency, the fraction of the input voltage that appears across each component changes with frequency. Taking the output across the capacitor produces a low-pass filter: the capacitor blocks high-frequency currents, so high-frequency signals are mostly dropped across the resistor and do not appear at the output. Swapping the output to the resistor gives a high-pass filter that blocks DC and attenuates low-frequency signals while allowing high-frequency signals to pass.
The cutoff frequency formula: fc = 1 / (2 x pi x R x C)
The cutoff frequency (also called the -3 dB frequency or corner frequency) is the frequency at which the filter transitions from passing to attenuating. At exactly fc, the output voltage is 1/sqrt(2) of the input voltage, which equals approximately 0.707 or -3.01 dB. At this frequency, the capacitive reactance Xc = 1/(2pifc x C) equals R, so exactly half the input power is dissipated in each component. The RC time constant tau = R x C (measured in seconds) is the reciprocal of the angular cutoff frequency: tau = 1/(2pi x fc). This is also the time for the capacitor to charge to 63.2% of an applied step voltage. Beyond the cutoff, gain rolls off at -20 dB per decade (a factor of 10 in frequency gives a factor of 10 reduction in voltage).
Gain, attenuation and phase shift at any frequency
The gain of a low-pass RC filter at any frequency f is |H(f)| = 1 / sqrt(1 + (f/fc)^2). The phase shift (lag) is phi = -arctan(f/fc). For a high-pass filter the gain is |H(f)| = (f/fc) / sqrt(1 + (f/fc)^2) and the phase lead is phi = +arctan(fc/f). At a frequency of 10 x fc (one decade above cutoff), a low-pass filter attenuates to 0.0995 of the input (-20 dB). At 100 x fc (two decades), it is down to 0.01 (-40 dB). Enter your signal frequency in this calculator to find the exact gain in linear and dB form, plus the phase angle.
Practical design tips and applications
RC filters appear in audio tone controls, anti-aliasing filters before analog-to-digital converters, power supply decoupling, RF noise suppression, and signal conditioning. A common design workflow: choose the cutoff frequency based on what you want to pass, select a standard capacitor value from the E12 series (e.g. 10 nF, 100 nF), then use the solve-for-R mode to find the required resistance and pick the nearest E24 standard value. Alternatively, fix R at a convenient value and solve for C. For tighter roll-off without an active op-amp, cascade two identical RC stages. Note that loading effects mean the effective cutoff of a two-stage cascade differs slightly from that of a single stage, so the combined -3 dB point is approximately fc / 0.6436 relative to the individual stage fc.
Gain and phase shift at common frequency ratios (first-order RC filter)
| f / fc | Gain (linear) | Gain (dB) | Phase (LP) | Phase (HP) |
|---|---|---|---|---|
| 0.01 | 1.0000 | 0.00 dB | -0.57 deg | +89.43 deg |
| 0.1 | 0.9950 | -0.04 dB | -5.71 deg | +84.29 deg |
| 0.5 | 0.8944 | -0.97 dB | -26.57 deg | +63.43 deg |
| 1.0 (cutoff) | 0.7071 | -3.01 dB | -45.00 deg | +45.00 deg |
| 2.0 | 0.4472 | -6.99 dB | -63.43 deg | +26.57 deg |
| 10 | 0.0995 | -20.04 dB | -84.29 deg | +5.71 deg |
| 100 | 0.0100 | -40.00 dB | -89.43 deg | +0.57 deg |
f/fc is the ratio of your signal frequency to the cutoff frequency. Values apply to both low-pass and high-pass filters relative to their pass bands. Phase sign is for low-pass (high-pass has opposite sign).
Frequently asked questions
What does the -3 dB cutoff frequency of an RC filter mean?
The -3 dB cutoff frequency is the frequency at which the output voltage drops to 0.707 (1/sqrt(2)) of the input voltage. At this point the output power is exactly half of the input power (since power is proportional to voltage squared). Frequencies beyond the cutoff are increasingly attenuated: at 10 x fc the gain is about 0.1 (-20 dB), and at 100 x fc it is about 0.01 (-40 dB).
How do I choose resistor and capacitor values for a given cutoff frequency?
Use the formulas R = 1/(2 x pi x fc x C) or C = 1/(2 x pi x fc x R). The easiest workflow is to pick a standard capacitor value first (e.g. 10 nF from the E12 series) and solve for the required R, then select the nearest E24 or E96 standard resistor. For example, for fc = 1 kHz with C = 10 nF: R = 1/(2pi x 1000 x 10e-9) = 15,915 Ohm. Use 16 kOhm (nearest E24 value), giving an actual cutoff of 995 Hz, less than 1% off. Use the "Solve for R" or "Solve for C" mode in this calculator to skip the arithmetic.
What is the RC time constant?
The time constant tau = R x C is the time for the capacitor voltage to reach 63.2% of a step input voltage (one e-folding time). After 5 x tau (five time constants) the voltage is more than 99% of the final value and the circuit is considered settled. The time constant and the cutoff frequency are related by tau = 1/(2 x pi x fc), so a filter with tau = 1 ms has a cutoff at about 159 Hz.
How much phase shift does an RC filter introduce?
Phase shift depends on the ratio of your signal frequency to the cutoff frequency. For a low-pass RC filter the output lags the input by arctan(f/fc) degrees. At fc the lag is 45 degrees. Well above fc it approaches 90 degrees. For a high-pass filter the output leads the input by arctan(fc/f) degrees, reaching +45 degrees at fc and approaching 0 degrees at high frequencies. Use this calculator to find the exact phase at any signal frequency.
What is the roll-off rate of a single RC filter stage?
A single-stage RC filter rolls off at -20 dB per decade beyond the cutoff frequency. This means that for every factor of 10 increase in frequency (above the cutoff for low-pass, or below the cutoff for high-pass), the gain drops by 20 dB (a factor of 10 in voltage). For steeper attenuation, cascade two stages to get -40 dB/decade, or use an active filter with an op-amp.
What is the difference between a low-pass and high-pass RC filter circuit?
In a low-pass RC filter (R in series, C to ground), the output is taken across the capacitor. The capacitor has high impedance at low frequencies, so most voltage appears at the output. At high frequencies its impedance drops, and most voltage falls across R instead. In a high-pass RC filter (C in series, R to ground), the output is taken across the resistor. The capacitor blocks DC and low-frequency signals, while high-frequency signals pass through with little loss.
Can I build a band-pass filter from RC components?
Yes. Connecting a high-pass RC stage in series with a low-pass RC stage creates a passive RC band-pass filter. The lower cutoff is set by the high-pass stage (fc_HP) and the upper cutoff by the low-pass stage (fc_LP). The filter passes frequencies between fc_HP and fc_LP. The bandwidth is fc_LP minus fc_HP. For a well-defined passband, choose fc_LP at least one decade above fc_HP, otherwise the two stages interact and the center-frequency gain is significantly reduced.